Search for anomalous weak dipole moments of the $\tau$ lepton

The anomalous weak dipole moments of the $\tau$ lepton are measured in a data sample collected by ALEPH from 1990 to 1995 corresponding to an integrated luminosity of 155~pb$^{-1}$. Tau leptons produced in the reaction $e^+ e^- \rightarrow \tau^+ \tau^-$ at energies close to the ${\rm Z}$ mass are studied using their semileptonic decays to $\pi$, $\rho$, $a_1 \rightarrow \pi 2\pi^0$ or $a_1 \rightarrow 3 \pi$. The real and imaginary components of both the anomalous weak magnetic dipole moment and the CP-violating anomalous weak electric dipole moment, $ {\rm Re}\,\mu_{\tau}$, ${\rm Im}\,\mu_{\tau}$, ${\rm Re}\,d_{\tau}$ and ${\rm Im}\,d_{\tau}$, are measured simultaneously by means of a likelihood fit built from the full differential cross section. No evidence of new physics is found. The following bounds are obtained (95\% CL): $|{\rm Re}\, \mu_{\tau} | 1.14 \times 10^{-3}$, $|{\rm Im}\, \mu_{\tau} | 2.65 \times 10^{-3}$, $|{\rm Re}\, d_{\tau} | 0.91 \times 10^{-3}$, and $|{\rm Im}\, d_{\tau} | 2.01 \times 10^{-3}$